I would lean towards solution 2. It's a good idea, less confusing than my "effective volume", for similar effects.
Ringworlds are meant to be awe-inspiring. Each arc needing a small squadron to outfight it seems fitting. Larger worlds, ringworlds especially, tend not to have the rarest resources anyway.
You get a nice dynamic where you're forced to expand to secure rare resources with lots of small outlying colonies. But you can afford to focus creative and aesthetic effort on a small number of beautiful and truly sprawling core worlds without losing out strategically.
(Earth size has always been a useful base for various things. It would be a consistent approach. I don't know that large worlds are the base for anything at the moment? Linear scaling is only really necessary if you are treating every planet physically as Trantor, with every inch of area built on. Otherwise, it can be more balance-based)
Ringworlds are meant to be awe-inspiring. Each arc needing a small squadron to outfight it seems fitting. Larger worlds, ringworlds especially, tend not to have the rarest resources anyway.
You get a nice dynamic where you're forced to expand to secure rare resources with lots of small outlying colonies. But you can afford to focus creative and aesthetic effort on a small number of beautiful and truly sprawling core worlds without losing out strategically.
(Earth size has always been a useful base for various things. It would be a consistent approach. I don't know that large worlds are the base for anything at the moment? Linear scaling is only really necessary if you are treating every planet physically as Trantor, with every inch of area built on. Otherwise, it can be more balance-based)